Multilevel sequential Monte Carlo: Mean square error bounds under verifiable conditions

Abstract : In this article, we consider the multilevel sequential Monte Carlo (MLSMC) method of Beskos et al. (Stoch. Proc. Appl. [to appear]). This is a technique designed to approximate expectations w.r.t. probability laws associated to a discretization. For instance, in the context of inverse problems, where one discretizes the solution of a partial differential equation. The MLSMC approach is especially useful when independent, coupled sampling is not possible. Beskos et al. show that for MLSMC the computational effort to achieve a given error, can be less than independent sampling. In this article we significantly weaken the assumptions of Beskos et al., extending the proofs to non-compact state-spaces. The assumptions are based upon multiplicative drift conditions as in Kontoyiannis and Meyn (Electron. J. Probab. 10 [2005]: 61–123). The assumptions are verified for an example.
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Submitted on : Wednesday, December 20, 2017 - 3:53:23 PM
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Pierre Del Moral, Ajay Jasra, Kody J. H. Law. Multilevel sequential Monte Carlo: Mean square error bounds under verifiable conditions. Stochastic Analysis and Applications, Taylor & Francis: STM, Behavioural Science and Public Health Titles, 2016, 35 (3), pp.478 - 498. ⟨10.1080/07362994.2016.1272421⟩. ⟨hal-01669155⟩

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